<h2>Problem 296</h2>
<div style="color:#666;font-size:80%;">11 June 2010</div><br />
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<p>
Given is an integer sided triangle <var>ABC</var> with <var>BC</var> <img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' /> <var>AC</var> <img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' /> <var>AB</var>.<BR />
<var>k</var> is the angular bisector of angle <var>ACB</var>.<BR /> <var>m</var> is the tangent at <var>C</var> to the circumscribed circle of <var>ABC</var>.<BR /> <var>n</var> is a line parallel to <var>m</var> through <var>B</var>.<BR />
The intersection of <var>n</var> and <var>k</var> is called <var>E</var>.
</p>
<div align='center'><img src="project/images/p296_bisector.gif" /></div>
<p>
How many triangles <var>ABC</var> with a perimeter not exceeding 100 000 exist such that <var>BE</var> has integral length?
</p>


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